Name
Abstract | ||
|---|---|---|
We study the problem of determining the size of the largest intersecting P-free family for a given partially ordered set (poset) P. In particular, we find the exact size of the largest intersecting B-free family where B is the butterfly poset and classify the cases of equality. The proof uses a new generalization of the partition method of Griggs, Li and Lu. We also prove generalizations of two well-known inequalities of Bollobás and Greene, Katona and Kleitman in this case. Furthermore, we obtain a general bound on the size of the largest intersecting P-free family, which is sharp for an infinite class of posets originally considered by Burcsi and Nagy, when n is odd. Finally, we give a new proof of the bound on the maximum size of an intersecting k-Sperner family and determine the cases of equality. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.jcta.2017.04.009 | Journal of Combinatorial Theory, Series A |
Keywords | DocType | Volume |
Intersecting set family,Forbidden poset,Butterfly,Sperner,Antichain | Journal | 151 |
ISSN | Citations | PageRank |
0097-3165 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dániel Gerbner | 1 | 46 | 21.61 |
| Abhishek Methuku | 2 | 18 | 9.98 |
| Casey Tompkins | 3 | 0 | 0.68 |